Species evolution is a topic where concepts of continuity and discontinuity have been opposed for two centuries. What is the situation today in biological evolution ? The statistical distribution of appearances and disappearances among rodent species follows power laws, suggesting nonlinearity and fractal structures. Thus, the domain of living beings seems to be extended, through critical physical phenomena, to the analysis of linear versus nonlinear biological phenomena. These observations are consistent with the new scale relativity theory of Nottale, which predicts many domains of resolution in nature separated by scale dependence or scale independence. Despite some scale-dependence particular to various levels of biological organization, the fact that they are also characterized by scale-independence suggests that they could be described by new fundamental laws revealing their potentially fractal and irreversible character. In the proximity of the critical time, specific to each system, the system becomes unstable and fractal, and shows precursor events at an accelerated rate leading up to the critical time. After the critical time, the system shows replicate events, in a decelerating manner. The discontinuous appearance of a number of clades follows a log-periodic law with a middle scale report of 1.73. This law, first applied to earthquakes, stock market crashes, demography, and physical turbulences, and now also being applied with success to macroevolutionary patterns, seems to have a certain universality.
Evolution, continuity, discontinuity, linear, nonlinear, scale relativity